Seismic Benefits of a Vibrating Mass Equipped with an Inerter on Frame Structures Due to Soil Interaction

The reduction of the seismic effects on new and existing structures is a relevant topic of the structural mechanics applied to the civil engineering. Usually, the conceptual aspects related to a new approach are studied by means of low-dimensional mechanical models able to capture the main dynamic aspects of the method. The present paper can be framed in this context. Specifically, the paper investigates the possibility of reducing the seismic response of a frame structure by using a vibrating mass connected to an inerter device, which interacts through the soil to protect the structure. The problem is studied by using existing soil–structure interaction (SSI) and structure–soil–structure interaction (SSSI) models, which describe the actions between the structure and the soil, and among adjacent structures through linear visco-elastic devices. A seven-degrees-of-freedom mechanical model is used to describe the problem, where a general multi-story frame structure is mathematically described by means of an equivalent 2-degrees-of-freedom system. The external vibrating mass is coupled with the inerter device to increase its inertia without using high real mass. The aim of the paper is to point out the role of the many parameters that characterize the interaction system. Particular attention is devoted to the mechanical characteristics of the soil, in order to know the effectiveness of the SSSI system as a function of the characteristics of the soil. Results show that the vibrating mass equipped with the inerter device is almost always beneficial for the frame structure to be protected. However, sufficient good performances justifying the costs of this method can be reached only in limited ranges of the characterizing parameters.